Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
Archivum Mathematicum (2016)
- Volume: 052, Issue: 4, page 207-219
- ISSN: 0044-8753
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topKhanh, Nguyen Ngoc. "Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds." Archivum Mathematicum 052.4 (2016): 207-219. <http://eudml.org/doc/287560>.
@article{Khanh2016,
abstract = {In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds $(M,g)$ for the following general heat equation \[ u\_t=\Delta \_V u+au\log u+bu \]
where $a$ is a constant and $b$ is a differentiable function defined on $M\times [0, \infty )$. We suppose that the Bakry-Émery curvature and the $N$-dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.},
author = {Khanh, Nguyen Ngoc},
journal = {Archivum Mathematicum},
keywords = {gradient estimates; general heat equation; Laplacian comparison theorem; $V$-Bochner-Weitzenböck; Bakry-Emery Ricci curvature},
language = {eng},
number = {4},
pages = {207-219},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds},
url = {http://eudml.org/doc/287560},
volume = {052},
year = {2016},
}
TY - JOUR
AU - Khanh, Nguyen Ngoc
TI - Gradient estimates of Li Yau type for a general heat equation on Riemannian manifolds
JO - Archivum Mathematicum
PY - 2016
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 052
IS - 4
SP - 207
EP - 219
AB - In this paper, we consider gradient estimates on complete noncompact Riemannian manifolds $(M,g)$ for the following general heat equation \[ u_t=\Delta _V u+au\log u+bu \]
where $a$ is a constant and $b$ is a differentiable function defined on $M\times [0, \infty )$. We suppose that the Bakry-Émery curvature and the $N$-dimensional Bakry-Émery curvature are bounded from below, respectively. Then we obtain the gradient estimate of Li-Yau type for the above general heat equation. Our results generalize the work of Huang-Ma ([4]) and Y. Li ([6]), recently.
LA - eng
KW - gradient estimates; general heat equation; Laplacian comparison theorem; $V$-Bochner-Weitzenböck; Bakry-Emery Ricci curvature
UR - http://eudml.org/doc/287560
ER -
References
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